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30 May 2024, 12:29
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C
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Difficulty:
45%
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Question Stats:
72% (02:31) correct
28%
(02:17)
wrong
based on 1187
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A movie theater increased the ticket price for evening shows by 10% and decreased the ticket price for morning shows by 40%. The average number of tickets sold for the morning shows increased by 30%, and the average number of tickets sold for the evening shows decreased by 5%. What was the percentage change in total revenue?
(1) Prior to the changes in ticket prices, the ticket prices for the morning shows and the evening shows were the same.
(2) Prior to the changes in ticket prices, the ratio between the number of tickets sold for the morning shows and the evening shows was 5:8.
(1) Prior to the changes in ticket prices, the ticket prices for the morning shows and the evening shows were the same.
(2) Prior to the changes in ticket prices, the ratio between the number of tickets sold for the morning shows and the evening shows was 5:8.
11 Nov 2024, 04:22
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guddo
You don't need to calculate anything here. I will use variables to show you the logic though you shouldn't need to use any of the steps given below.
Video solution to this problem: https://youtu.be/wFor-e2sYHg
Think about it: Total Revenue is given by Price * Quantity
\(R_{old} = Pm*Qm + Pe*Qe\)
For new revenue, all these variables on the right hand side have increased or decreased by a percentage (I don't care by how much but I am still writing them down here)
\(R_{new} = 0.6Pm * 1.3Qm + 1.1Pe * .95Qe\)
Percentage change = \(\frac{R_{new} }{ R_{old}} - 1 = \frac{0.6Pm * 1.3Qm + 1.1Pe * .95Qe }{ Pm*Qm + Pe*Qe} - 1\)
So we need to know the value of the variables.
(1) Prior to the changes in ticket prices, the ticket prices for the morning shows and the evening shows were the same.
This tells us that Pm = Pe. So we will be able to replace both by simply P and the P term will cancel off in the numerator and denominator. But we still do not know the Qm and Qe.
(2) Prior to the changes in ticket prices, the ratio between the number of tickets sold for the morning shows and the evening shows was 5:8.
This tells us that Qm = 5x and Qe = 8x. So we can replace all Q with the x terms and the x terms of numerator and denominator will cancel off but we will still have all Pm and Pe.
Using both, all our variables would be gone so we will be able to calculate the % change.
Answer (C)
Video on percentages: https://youtu.be/HxnsYI1Rws8
General Discussion
31 May 2024, 16:12
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Bunuel
\(x =#\) of morning tickets, \( y = #\) of evening tickets
\(m=\) moring ticket price, \(e = \)evening ticket price
Old revenue = \(x*m + y*e\) ..(i)
New Revenue = \(1.3x *.6m +.95y*1.1e\)..(ii)
% Change in revenue = \(\frac{ (ii ) -(i) }{(i)}\) = \(\frac{ (.22xm) -(.045ye) }{(x*m + y*e)}\)...(i)
(1) Prior to the changes in ticket prices, the ticket prices for the morning shows and the evening shows were the same
\(m = e \)
Substituing in ...(i)
\(\frac{ (.22xm) -(.045ym) }{(x*m + y*m)}\).
\(\frac{ (.22x) -(.045y) }{(x + y)}\).
Clearly still INSUFF.
(2) Prior to the changes in ticket prices, the ratio between the number of tickets sold for the morning shows and the evening shows was 5:8
Let \(#\) of morning tickets \(x = 5p\) and \(#\) of evening tickets \(y = 8p \)
Substituing in ...(i)
\(\frac{ (.22*5pm) -(.045*8pe) }{(5p*m + 8p*e)}\)
\(\frac{ (1.1m) -(.36e) }{(5m + 8e)}\)
INSUFF.
1+2
From statement (2) we have \(\frac{ (1.1m) -(.36e) }{(5m + 8e)}\)
From statement (1) we have \(m=e \)
Therefore % change \(\frac{ (1.1m) -(.36m) }{(5m + 8m)}\)
SUFF.
Ans C
Hope it helped.
